| Project/Area Number |
25400035
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo University of Agriculture and Technology |
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Principal Investigator |
Hara Nobuo 東京農工大学, 工学(系)研究科(研究院), 教授 (90298167)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 代数幾何 / 正標数 / フロベニウス直像 / F爆発 / 大域的F有限型 / 大域的F正則 / 特異点 / ベクトル束 / 大域的有限F表現型 / フロベニウス写像 |
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| Outline of Final Research Achievements |
We studied the Frobenius push-forwards on algebraic varieties and their singularities in positive characteristic p, focusing on a few classes of projective varieties and normal surface singularities. Our results are as follows.
1. We classified the structure of the F-blowup sequence of a simple elliptic singularity in terms of the characteristic p, the self-intersection number of the exceptional elliptic curve E on the minimal resolution, and whether E is ordinary or supersingular.
2. We studied the Frobenius push-forward of the structure sheaf of the surface obtained by blowing up the projective plane at n points in general position. In case n=4 (del Pezzo surface of degree 5), we determined all the indecomposable direct summands of the iterated Frobenius push-forwards, and proved that their isomorphism classes are finite (GFFRT). We also proved that these Frobenius summands generate the derived category in case n=4. In case n=10, we constructed a rational surface that is not GFFRT.
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